﻿using System.Collections.Generic;

namespace ProblemsSet
{
    public class Problem_29 : BaseProblem
    {
        public override object GetResult()
        {
            const long maxA = 100;
            const long maxB = 100;
            var res = new HashSet<string>();

            for (var a = 2; a <= maxA; a++ )
            {
                var tmp = MathLogic.GetPrimeFactors(a);
                for (var b = 2; b <= maxB; b++)
                {
                    var tmp2 = "";
                    foreach (var pair in tmp)
                    {
                        tmp2 += pair.Key + "^" + b*pair.Value + "*";
                    }
                    if (!res.Contains(tmp2)) res.Add(tmp2);
                }
            }

            return res.Count;
        }


        public override string Problem
        {
            get
            {
                return @"Consider all integer combinations of ab for 2  a  5 and 2  b  5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2  a  100 and 2  b  100?";
            }
        }

        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return 9183;
            }
        }
    }
}
